Preheat broiler with a rack 6 inches from heat source. Arrange tomatillos, chiles, garlic cloves, and onion wedges on a large rimmed baking sheet covered with foil. Drizzle vegetables evenly with oil. Broil until charred, about 12 minutes, flipping vegetables halfway through cooking time. Remove and discard charred papery skin from onion. Transfer vegetables and juices to a medium bowl, and cover using plastic wrap; let steam 10 minutes. Heat oven to 425°F.

Meanwhile, stir together chili powder, cumin, coriander, and 1 ¾ teaspoons salt in a small bowl. Arrange chicken breasts on a cutting board; slice each breast horizontally through the middle to within a ½-inch of other side. Open chicken breasts, and sprinkle evenly with 2 teaspoons spice mixture.

Once vegetables are steamed, remove and discard garlic and chile peels. Transfer peeled garlic, 1 peeled chile, tomatillos, onion, and any accumulated juices to a blender; add cilantro and remaining ¾ teaspoon salt. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening; process until smooth, about 30 seconds. Pour into a large ovenproof skillet. Set aside.

Slice remaining peeled chile lengthwise into thin strips. Cut cream cheese into 4 equal slices; place 1 slice on one-half of each butterflied chicken breast. Top evenly with sliced chile, and close chicken breast. Sprinkle remaining 2 teaspoons spice mixture all over chicken; nestle stuffed breasts into sauce in skillet.

Bake until sauce is bubbly and a thermometer inserted into thickest portion of breasts registers 160°F, 20 to 25 minutes. Remove skillet from oven, and increase oven temperature to broil.

Sprinkle chicken and sauce with cheese. Broil until cheese is melted and starting to brown in spots, 2 to 3 minutes. Remove from oven, and garnish with avocado and additional cilantro. Serve with lime wedges.